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Uncertainty Principle

  The uncertainty principle is one of the most important consequences of quantum mechanics. In its most general form, it states the accuracy with which we may carry out a measurement of two properties of a system. This will be determined by a mathematical relationship between the two properties. The most common pair of measurable properties that we apply this principle to are position and momentum.

We may understand the position-momentum uncertainty principle if we think about trying to accurately measure the position of a particle. If we wish to see where the particle is, we must shine light on it. Only by detecting the light which is reflected from its surface may we know its position. However, light may be thought of as being composed of particles itself, called photons. Each photon possesses momentum of its own, and when it strikes the particle, it gives the particle a small ‘kick’. Thus by measuring its position accurately, we have altered its momentum. We can never measure the position of the particle without imparting an uncertain amount of momentum to it. It is possible to show by similar arguments that we cannot measure momentum without increasing the position uncertainty.

The mathematical statement of the position-momentum uncertainty principle is the equationΔxΔpx≥ħ/2Here x is the uncertainty in position, px the uncertainty in momentum, and h is a very small number, 6 × 10-34, known as Planck\'s constant. The fact that Planck\'s constant is so very small is the reason that we never come across the effect in our everyday lives.

Recently it has been proposed that it may be possible to do better than the uncertainty principle in some parts of a system, at the expense of greater uncertainty in other parts of the system. This process is known as ‘squeezed states’, and initial results are promising. JJ

See also de Broglie waves; quantum theory; wave-particle duality of light.



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